22-23 Geom B Unit 4 Portfolio, im really struggling and the videos dont help, its already overdue, can anyone walk me through the problems or even better walk me through to the awnser please? ^^

Answer 1

Problem 1:

Given: Triangle ABC with AB = 8, BC = 10, and AC = 12

Find: The measure of angle A

Solution:

We can use the Law of Cosines to solve for angle A.

The Law of Cosines states that:

c^2 = a^2 + b^2 - 2abcos(C)

Where c is the longest side of the triangle, a and b are the other two sides, and C is the angle opposite side c.

In this case, c = 12, a = 8, and b = 10.

So, we have:

12^2 = 8^2 + 10^2 - 2(8)(10)cos(A)

144 = 64 + 100 - 160cos(A)

80 = 160cos(A)

cos(A) = 0.5

Now, we can use the inverse cosine function to find the measure of angle A.

A = cos^-1(0.5)

A = 60°

Answer 2

Right idea by the bot, but wrong execution
the side opposite angle A has length 10

so
10^2 = 8^2 + 12^2 - 2(8)(12)cosA
cosA = 108/192
angle A = appr 55.8°

On top of that, the bot made an error in its arithmetic.
"144 = 64 + 100 - 160cos(A)"
should have given it
160cosA = 20